My research interests primarily lie in the analysis of partial differential equations, mathematical finance, and mean field theory.
Specifically, I focus on the mathematics of liquid crystals, portfolio selection in financial markets, and mean field game/control problems.
Publications/ Preprints:
(9). Viscosity solutions of fully second-order HJB equations in the Wasserstein space,
with Erhan Bayraktar, Hang Cheung, Ibrahim Ekren, Jinniao Qiu and Xin Zhang,
submitted, preprint available here (2025).
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(8). A variational approach to portfolio choice,
with Paolo Guasoni and Emmet Lawless,
submitted (2024).
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(7). Incentives of defined-contribution pension managers,
with Paolo Guasoni, Bohan Li, Tak Kwong Wong and Sheung Chi Phillip Yam,
submitted (2024).
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(6). A control theoretical approach to mean field games. Part II: global well-posedness of master equation,
with Alain Bensoussan, Tak Kwong Wong and Sheung Chi Phillip Yam,
to appear in Applied Mathematics and Optimization, preprint available here (2024).
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(5). A control theoretical approach to mean field games. Part I: global equilibrium solution, [Article]
with Alain Bensoussan, Tak Kwong Wong and Sheung Chi Phillip Yam,
Applied Mathematics and Optimization 92(44) (2025).
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(4). Mean field type control problems, some Hilbert-space-valued FBSDEs, and related equations, [Article]
with Alain Bensoussan and Sheung Chi Phillip Yam,
ESAIM: Control, Optimisation and Calculus of Variations 31:33 (2025).
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(3). Viscosity solutions of a class of second order Hamilton-Jacobi-Bellman equations in the Wasserstein space, [Article]
with Hang Cheung and Jinniao Qiu,
Applied Mathematics and Optimization 91(23) (2025).
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(2). Pattern formation in Landau-de Gennes theory, [Article]
with Yong Yu,
Journal of Functional Analysis 285(1), 109923 (2023).
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(1). Singular solutions to some semilinear elliptic equations: an approach of Born-Infeld approximation, [Article]
with Chia-Yu Hsieh and Yong Yu,
Communications in Mathematical Sciences 19(2), 557–584 (2021).